Let X be a r.v. with d.f. F; i.e., F(x) = P(X ( x), x ( (.

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Let X be a r.v. with d.f. F; i.e., F(x) = P(X ( x), x ( (. Then show that
(i) P(X < x) = F(x -) (the left-hand side limit).
(ii) F(x) is continuous at x if and only if P(X = x) = 0.

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An Introduction to Measure Theoretic Probability

ISBN: 978-0128000427

2nd edition

Authors: George G. Roussas

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Question Posted: Mar 25, 2016 03:31 AM

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Let X be a r.v. with d.f. F; i.e., F(x) = P(X ( x), x ( (.

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i Let xn 0 as n and define the events An X x xn A X x Then clearly as n An a...View the full answer

An Introduction to Measure Theoretic Probability

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